Finance 2 (2023) – Problem Set 2
University of Amsterdam
Answers to IN CLASS exercises do not need to be handed in
The parts of exercises marked [IN CLASS] (e.g. 1d) will be completed during the tutorial and
answers to these parts do not need to be handed in via Canvas. Answers to the other
questions need to be completed before the deadline (see Canvas) and students need them to
participate in the tutorial.
Grading: only first problem set and bonus
We will only grade the first homework set in Canvas and then at the end of the course
determine if you have received the bonus or not. You will therefore not see a grade for each
homework set you have handed in. Feedback is possible during the tutorials.
Question 1 | Chapter 14 – Capital Structure and Modigliani-Miller
PT corporation is currently an all-equity firm with an expected return of 13%. It is considering a
leveraged recapitalization in which it would borrow and repurchase existing shares. Assume
perfect capital markets.
a. Suppose PT borrows to the point that its debt-equity ratio is 0.50. With this amount of
debt, the debt cost of capital is 6%. What will the expected return of equity be after this
transaction?
b. Suppose instead PT borrows to the point that its debt-equity ratio is 1.50. With this
amount of debt, PT’s debt will be riskier and as a result, the debt cost of capital will
increase to 7%. What will the expected return of equity be in this case?
c. A senior manager argues that it is in the best interest of the shareholders to choose the
capital structure that leads to the highest expected return for the stock. How would you
respond to this argument?
d. Explain the concept of homemade leverage. How does this concept relate to the link
between capital structure and the value of the firm? [IN CLASS]
Question 2 | Chapter 14 - Capital Structure and Modigliani-Miller
In mid-2015, Qualcomm Inc. had $11 billion in debt, total equity capitalization of $89 billion,
and an equity beta of 1.43 (as reported on Yahoo! Finance). Included in Qualcomm’s assets
was $21 billion in cash and risk-free securities. Assume that the risk-free rate of interest is 3%,
the market risk premium is 4% and that the debt is risk-free. Also assume perfect capital
markets.
a. What is Qualcomm’s enterprise value?
b. What is the beta of Qualcomm’s business assets?
c. What is Qualcomm’s WACC which can be used to evaluate projects with similar risk as
Qualcomm’s existing business activities?
1
,Question 3 | Chapter 15 - Capital Structure and interest tax shields
RE corporation maintains a debt-equity ratio of 0.88, has an equity cost of capital of 14%, and
a debt cost of capital of 6.5%. RE’s corporate tax rate is 35%, and its market capitalization is
$240 million. Assume the firm has no excess cash and that taxes are the only capital market
imperfection.
a. What is RE’s after-tax WACC?
b. RE’s yearly free cash flow is expected to be $10 million one year from now and the market
assumes this cash flow will continue forever growing at a fixed rate. What constant
expected future growth rate is consistent with the firm’s current market value?
c. Estimate the present value of RE’s interest tax shield.
d. What is the present value of RE’s interest tax shield if instead of maintaining a fixed debt-
equity ratio the firm would hold a fixed amount of $150 million in debt? [IN CLASS]
e. Can you explain in words why there is a significant difference between the answers to c
and d? [IN CLASS]
f. Does increasing the corporate profit tax rate increase the interest tax shield? What about
the value of the firm? [IN CLASS]
2
, Problem set 2
Question 1
PT corporation is currently an all-equity firm with an expected return of 13%. It is
considering a leveraged recapitalization in which it would borrow and repurchase
existing shares. Assume perfect capital markets.
a.
Expected return on equity: since PT is an all-equity firm, rᵤ = rₐ = 13%.
rₑ = 13% + 0.5 * (13% - 6%) = 16.5%
b.
Expected return on equity:
rₑ = 13% + 1.5 * (13% - 7%) = 22.0%
c.
According to the first proposition of Modigliani-Miller, the capital structure does not
have an effect on the value of a firm. The riskiness of the assets remain the same
regardless of how risk is distributed among the debt and equity. The leverage does not
affect the total value of the firm, it only changes the allocation of cash flows between
debt and equity. Therefore, it does not matter what kind of capital structure is chosen by
the shareholders.
University of Amsterdam
Answers to IN CLASS exercises do not need to be handed in
The parts of exercises marked [IN CLASS] (e.g. 1d) will be completed during the tutorial and
answers to these parts do not need to be handed in via Canvas. Answers to the other
questions need to be completed before the deadline (see Canvas) and students need them to
participate in the tutorial.
Grading: only first problem set and bonus
We will only grade the first homework set in Canvas and then at the end of the course
determine if you have received the bonus or not. You will therefore not see a grade for each
homework set you have handed in. Feedback is possible during the tutorials.
Question 1 | Chapter 14 – Capital Structure and Modigliani-Miller
PT corporation is currently an all-equity firm with an expected return of 13%. It is considering a
leveraged recapitalization in which it would borrow and repurchase existing shares. Assume
perfect capital markets.
a. Suppose PT borrows to the point that its debt-equity ratio is 0.50. With this amount of
debt, the debt cost of capital is 6%. What will the expected return of equity be after this
transaction?
b. Suppose instead PT borrows to the point that its debt-equity ratio is 1.50. With this
amount of debt, PT’s debt will be riskier and as a result, the debt cost of capital will
increase to 7%. What will the expected return of equity be in this case?
c. A senior manager argues that it is in the best interest of the shareholders to choose the
capital structure that leads to the highest expected return for the stock. How would you
respond to this argument?
d. Explain the concept of homemade leverage. How does this concept relate to the link
between capital structure and the value of the firm? [IN CLASS]
Question 2 | Chapter 14 - Capital Structure and Modigliani-Miller
In mid-2015, Qualcomm Inc. had $11 billion in debt, total equity capitalization of $89 billion,
and an equity beta of 1.43 (as reported on Yahoo! Finance). Included in Qualcomm’s assets
was $21 billion in cash and risk-free securities. Assume that the risk-free rate of interest is 3%,
the market risk premium is 4% and that the debt is risk-free. Also assume perfect capital
markets.
a. What is Qualcomm’s enterprise value?
b. What is the beta of Qualcomm’s business assets?
c. What is Qualcomm’s WACC which can be used to evaluate projects with similar risk as
Qualcomm’s existing business activities?
1
,Question 3 | Chapter 15 - Capital Structure and interest tax shields
RE corporation maintains a debt-equity ratio of 0.88, has an equity cost of capital of 14%, and
a debt cost of capital of 6.5%. RE’s corporate tax rate is 35%, and its market capitalization is
$240 million. Assume the firm has no excess cash and that taxes are the only capital market
imperfection.
a. What is RE’s after-tax WACC?
b. RE’s yearly free cash flow is expected to be $10 million one year from now and the market
assumes this cash flow will continue forever growing at a fixed rate. What constant
expected future growth rate is consistent with the firm’s current market value?
c. Estimate the present value of RE’s interest tax shield.
d. What is the present value of RE’s interest tax shield if instead of maintaining a fixed debt-
equity ratio the firm would hold a fixed amount of $150 million in debt? [IN CLASS]
e. Can you explain in words why there is a significant difference between the answers to c
and d? [IN CLASS]
f. Does increasing the corporate profit tax rate increase the interest tax shield? What about
the value of the firm? [IN CLASS]
2
, Problem set 2
Question 1
PT corporation is currently an all-equity firm with an expected return of 13%. It is
considering a leveraged recapitalization in which it would borrow and repurchase
existing shares. Assume perfect capital markets.
a.
Expected return on equity: since PT is an all-equity firm, rᵤ = rₐ = 13%.
rₑ = 13% + 0.5 * (13% - 6%) = 16.5%
b.
Expected return on equity:
rₑ = 13% + 1.5 * (13% - 7%) = 22.0%
c.
According to the first proposition of Modigliani-Miller, the capital structure does not
have an effect on the value of a firm. The riskiness of the assets remain the same
regardless of how risk is distributed among the debt and equity. The leverage does not
affect the total value of the firm, it only changes the allocation of cash flows between
debt and equity. Therefore, it does not matter what kind of capital structure is chosen by
the shareholders.
